Borel set, criterion for a

From Encyclopedia of Mathematics
Jump to: navigation, search

A necessary and sufficient condition for an $\mathcal{A}$-set in a complete separable metric space to be a Borel set. Two criteria can be stated as follows: 1) its complement must also be an $\mathcal{A}$-set (Suslin's criterion); and 2) it can be represented as the union of non-intersecting components (Luzin's criterion).

How to Cite This Entry:
Borel set, criterion for a. Encyclopedia of Mathematics. URL:,_criterion_for_a&oldid=35729
This article was adapted from an original article by A.G. El'kin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article